Problem: Simplify the following expression: $\dfrac{16n^3}{32n^5}$ You can assume $n \neq 0$.
Solution: $ \dfrac{16n^3}{32n^5} = \dfrac{16}{32} \cdot \dfrac{n^3}{n^5} $ To simplify $\frac{16}{32}$ , find the greatest common factor (GCD) of $16$ and $32$ $16 = 2 \cdot 2 \cdot 2 \cdot 2$ $32 = 2 \cdot 2 \cdot 2 \cdot 2 \cdot 2$ $ \mbox{GCD}(16, 32) = 2 \cdot 2 \cdot 2 \cdot 2 = 16 $ $ \dfrac{16}{32} \cdot \dfrac{n^3}{n^5} = \dfrac{16 \cdot 1}{16 \cdot 2} \cdot \dfrac{n^3}{n^5} $ $\phantom{ \dfrac{16}{32} \cdot \dfrac{3}{5}} = \dfrac{1}{2} \cdot \dfrac{n^3}{n^5} $ $ \dfrac{n^3}{n^5} = \dfrac{n \cdot n \cdot n}{n \cdot n \cdot n \cdot n \cdot n} = \dfrac{1}{n^2} $ $ \dfrac{1}{2} \cdot \dfrac{1}{n^2} = \dfrac{1}{2n^2} $